Problem: Simplify the following expression: $z = \dfrac{4r + 3}{8r - 10} - \dfrac{6r + 12}{8r - 10}$
Solution: Since the expressions have the same denominator we simply subtract the numerators: $z = \dfrac{4r + 3 - (6r + 12)}{8r - 10}$ Distribute the negative sign: $z = \dfrac{4r + 3 - 6r - 12}{8r - 10}$ Combine like terms: $z = \dfrac{-2r - 9}{8r - 10}$